Open AccessStability analysis for a class of switched systems under perturbations with applications to consensus
Author(s) -
Wang Bo,
Tian YuPing
Publication year - 2017
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2016.1553
Subject(s) - mathematics , bounded function , multiplicative function , exponential stability , control theory (sociology) , topology (electrical circuits) , stability (learning theory) , consensus , martingale (probability theory) , convergence (economics) , multi agent system , computer science , mathematical analysis , combinatorics , nonlinear system , physics , control (management) , quantum mechanics , artificial intelligence , machine learning , economics , economic growth
This study investigates the stability problem for a class of discrete‐time switched systems with stochastic or non‐stochastic perturbations. Under the condition that the system matrix is weakly periodic and Hurwitz constrained, we firstly give stability analysis of the system with bounded or (exponentially) convergent perturbations. Then, for the system with perturbations containing stochastic noises, which are subject to a martingale‐difference assumption, we give mean square (m.s.) and almost sure (a.s.) convergence results. Both multiplicative noises and additive noises are discussed in this paper. As applications of the stability result, we give m.s. and a.s. consensus conditions for both multi‐agent systems (MASs) with relative‐state‐dependent noises and MASs with additive noises under the weakly periodic switching topology together with a Hurwitz constraint. Compared to the existing consensus results, we do not require the digraphs be balanced and the edge weights be non‐negative. We also give a more general form of the statistic properties of the final consensus point compared with the balanced switching topology case. Some examples are given to illustrate the effectiveness of the stability results and the consensus results.